Questions — Edexcel C1 (574 questions)

Browse by module
All questions AEA AS Paper 1 AS Paper 2 AS Pure C1 C12 C2 C3 C34 C4 CP AS CP1 CP2 D1 D2 F1 F2 F3 FD1 FD1 AS FD2 FD2 AS FM1 FM1 AS FM2 FM2 AS FP1 FP1 AS FP2 FP2 AS FP3 FS1 FS1 AS FS2 FS2 AS Further AS Paper 1 Further AS Paper 2 Discrete Further AS Paper 2 Mechanics Further AS Paper 2 Statistics Further Additional Pure Further Additional Pure AS Further Discrete Further Discrete AS Further Extra Pure Further Mechanics Further Mechanics A AS Further Mechanics AS Further Mechanics B AS Further Mechanics Major Further Mechanics Minor Further Numerical Methods Further Paper 1 Further Paper 2 Further Paper 3 Further Paper 3 Discrete Further Paper 3 Mechanics Further Paper 3 Statistics Further Paper 4 Further Pure Core Further Pure Core 1 Further Pure Core 2 Further Pure Core AS Further Pure with Technology Further Statistics Further Statistics A AS Further Statistics AS Further Statistics B AS Further Statistics Major Further Statistics Minor Further Unit 1 Further Unit 2 Further Unit 3 Further Unit 4 Further Unit 5 Further Unit 6 H240/01 H240/02 H240/03 M1 M2 M3 M4 M5 P1 P2 P3 P4 PMT Mocks PURE Paper 1 Paper 2 Paper 3 Pre-U 9794/1 Pre-U 9794/2 Pre-U 9794/3 Pre-U 9795 Pre-U 9795/1 Pre-U 9795/2 S1 S2 S3 S4 Unit 1 Unit 2 Unit 3 Unit 4
Browse by board
AQA AS Paper 1 AS Paper 2 C1 C2 C3 C4 D1 D2 FP1 FP2 FP3 Further AS Paper 1 Further AS Paper 2 Discrete Further AS Paper 2 Mechanics Further AS Paper 2 Statistics Further Paper 1 Further Paper 2 Further Paper 3 Discrete Further Paper 3 Mechanics Further Paper 3 Statistics M1 M2 M3 Paper 1 Paper 2 Paper 3 S1 S2 S3 CAIE FP1 FP2 Further Paper 1 Further Paper 2 Further Paper 3 Further Paper 4 M1 M2 P1 P2 P3 S1 S2 Edexcel AEA AS Paper 1 AS Paper 2 C1 C12 C2 C3 C34 C4 CP AS CP1 CP2 D1 D2 F1 F2 F3 FD1 FD1 AS FD2 FD2 AS FM1 FM1 AS FM2 FM2 AS FP1 FP1 AS FP2 FP2 AS FP3 FS1 FS1 AS FS2 FS2 AS M1 M2 M3 M4 M5 P1 P2 P3 P4 PMT Mocks PURE Paper 1 Paper 2 Paper 3 S1 S2 S3 S4 OCR AS Pure C1 C2 C3 C4 D1 D2 FD1 AS FM1 AS FP1 FP1 AS FP2 FP3 FS1 AS Further Additional Pure Further Additional Pure AS Further Discrete Further Discrete AS Further Mechanics Further Mechanics AS Further Pure Core 1 Further Pure Core 2 Further Pure Core AS Further Statistics Further Statistics AS H240/01 H240/02 H240/03 M1 M2 M3 M4 PURE S1 S2 S3 S4 OCR MEI AS Paper 1 AS Paper 2 C1 C2 C3 C4 D1 D2 FP1 FP2 FP3 Further Extra Pure Further Mechanics A AS Further Mechanics B AS Further Mechanics Major Further Mechanics Minor Further Numerical Methods Further Pure Core Further Pure Core AS Further Pure with Technology Further Statistics A AS Further Statistics B AS Further Statistics Major Further Statistics Minor M1 M2 M3 M4 Paper 1 Paper 2 Paper 3 S1 S2 S3 S4 Pre-U Pre-U 9794/1 Pre-U 9794/2 Pre-U 9794/3 Pre-U 9795 Pre-U 9795/1 Pre-U 9795/2 WJEC Further Unit 1 Further Unit 2 Further Unit 3 Further Unit 4 Further Unit 5 Further Unit 6 Unit 1 Unit 2 Unit 3 Unit 4
Sort by: Default | Easiest first | Hardest first
Edexcel C1 Q7
8 marks Moderate -0.8
Given that $$y = \sqrt{x} - \frac{4}{\sqrt{x}},$$
  1. find \(\frac{dy}{dx}\). [3]
  2. find \(\frac{d^2y}{dx^2}\). [2]
  3. show that $$4x\frac{d^2y}{dx^2} + 4x\frac{dy}{dx} - y = 0.$$ [3]
Edexcel C1 Q8
9 marks Moderate -0.3
  1. Prove that the sum of the first \(n\) positive integers is given by $$\frac{1}{2}n(n + 1).$$ [4]
  2. Hence, find the sum of
    1. the integers from 100 to 200 inclusive,
    2. the integers between 300 to 600 inclusive which are divisible by 3.
    [5]
Edexcel C1 Q9
10 marks Moderate -0.3
  1. Express each of the following in the form \(p + q\sqrt{2}\) where \(p\) and \(q\) are rational.
    1. \((4 - 3\sqrt{2})^2\)
    2. \(\frac{1}{2 + \sqrt{2}}\) [5]
    1. Solve the equation $$y^2 + 8 = 9y.$$
    2. Hence solve the equation $$x^3 + 8 = 9x^{\frac{1}{2}}.$$ [5]
Edexcel C1 Q10
13 marks Moderate -0.3
\includegraphics{figure_1} Figure 1 shows the curve with equation \(y = \text{f}(x)\). The curve meets the \(x\)-axis at the origin and at the point \(A\). Given that $$\text{f}'(x) = 3x^{\frac{1}{2}} - 4x^{-\frac{1}{2}},$$
  1. find f\((x)\). [5]
  2. Find the coordinates of \(A\). [2]
The point \(B\) on the curve has \(x\)-coordinate 2.
  1. Find an equation for the tangent to the curve at \(B\) in the form \(y = mx + c\). [6]
Edexcel C1 Q1
3 marks Moderate -0.8
Find the value of \(y\) such that $$4^{y + 3} = 8.$$ [3]
Edexcel C1 Q2
4 marks Easy -1.2
Find $$\int \left( 3x^2 + \frac{1}{2x^2} \right) dx.$$ [4]
Edexcel C1 Q3
6 marks Moderate -0.5
\includegraphics{figure_1} Figure 1 shows the rectangles \(ABCD\) and \(EFGH\) which are similar. Given that \(AB = (3 - \sqrt{5})\) cm, \(AD = \sqrt{5}\) cm and \(EF = (1 + \sqrt{5})\) cm, find the length \(EH\) in cm, giving your answer in the form \(a + b\sqrt{5}\) where \(a\) and \(b\) are integers. [6]
Edexcel C1 Q4
6 marks Moderate -0.3
  1. Sketch on the same diagram the curves \(y = x^2 - 4x\) and \(y = -\frac{1}{x}\). [4]
  2. State, with a reason, the number of real solutions to the equation $$x^2 - 4x + \frac{1}{x} = 0.$$ [2]
Edexcel C1 Q5
6 marks Moderate -0.3
  1. By completing the square, find in terms of the constant \(k\) the roots of the equation $$x^2 + 2kx + 4 = 0.$$ [4]
  2. Hence find the exact roots of the equation $$x^2 + 6x + 4 = 0.$$ [2]
Edexcel C1 Q6
7 marks Moderate -0.8
  1. Evaluate $$\sum_{r=1}^{50} (80 - 3r).$$ [3]
  2. Show that $$\sum_{r=1}^{n} \frac{r + 3}{2} = k n(n + 7),$$ where \(k\) is a rational constant to be found. [4]
Edexcel C1 Q7
7 marks Standard +0.3
Solve the simultaneous equations \begin{align} x - 3y + 7 &= 0
x^2 + 2xy - y^2 &= 7 \end{align} [7]
Edexcel C1 Q8
9 marks Moderate -0.3
Given that $$\frac{dy}{dx} = \frac{x^3 - 4}{x^2}, \quad x \neq 0,$$
  1. find \(\frac{d^2y}{dx^2}\). [3]
Given also that \(y = 0\) when \(x = -1\),
  1. find the value of \(y\) when \(x = 2\). [6]
Edexcel C1 Q9
13 marks Standard +0.3
A curve has the equation \(y = (\sqrt{x} - 3)^2\), \(x \geq 0\).
  1. Show that \(\frac{dy}{dx} = 1 - \frac{3}{\sqrt{x}}\). [4]
The point \(P\) on the curve has \(x\)-coordinate 4.
  1. Find an equation for the normal to the curve at \(P\) in the form \(y = mx + c\). [5]
  2. Show that the normal to the curve at \(P\) does not intersect the curve again. [4]
Edexcel C1 Q10
14 marks Standard +0.3
The straight line \(l\) has gradient 3 and passes through the point \(A(-6, 4)\).
  1. Find an equation for \(l\) in the form \(y = mx + c\). [2]
The straight line \(m\) has the equation \(x - 7y + 14 = 0\). Given that \(m\) crosses the \(y\)-axis at the point \(B\) and intersects \(l\) at the point \(C\),
  1. find the coordinates of \(B\) and \(C\), [4]
  2. show that \(\angle BAC = 90°\), [4]
  3. find the area of triangle \(ABC\). [4]
Edexcel C1 Q1
3 marks Easy -1.8
Evaluate \(49^{\frac{1}{2}} + 8^{\frac{1}{3}}\). [3]
Edexcel C1 Q2
4 marks Moderate -0.8
A sequence is defined by the recurrence relation $$u_{n+1} = \frac{u_n + 1}{3}, \quad n = 1, 2, 3, ...$$ Given that \(u_3 = 5\),
  1. find the value of \(u_4\), [1]
  2. find the value of \(u_1\). [3]
Edexcel C1 Q3
6 marks Moderate -0.8
\(\text{f}(x) = 4x^2 + 12x + 9\).
  1. Determine the number of real roots that exist for the equation \(\text{f}(x) = 0\). [2]
  2. Solve the equation \(\text{f}(x) = 8\), giving your answers in the form \(a + b\sqrt{2}\) where \(a\) and \(b\) are rational. [4]
Edexcel C1 Q4
6 marks Moderate -0.8
Find the set of values of \(x\) for which
  1. \(6x - 11 > x + 4\), [2]
  2. \(x^2 - 6x - 16 < 0\), [3]
  3. both \(6x - 11 > x + 4\) and \(x^2 - 6x - 16 < 0\). [1]
Edexcel C1 Q5
8 marks Moderate -0.8
\(\text{f}(x) = (2 - \sqrt{x})^2, \quad x > 0\).
  1. Solve the equation \(\text{f}(x) = 0\). [2]
  2. Find \(\text{f}(3)\), giving your answer in the form \(a + b\sqrt{3}\), where \(a\) and \(b\) are integers. [2]
  3. Find $$\int \text{f}(x) \, dx.$$ [4]
Edexcel C1 Q6
8 marks Moderate -0.8
The straight line \(l\) passes through the point \(P(-3, 6)\) and the point \(Q(1, -4)\).
  1. Find an equation for \(l\) in the form \(ax + by + c = 0\), where \(a\), \(b\) and \(c\) are integers. [4]
The straight line \(m\) has the equation \(2x + ky + 7 = 0\), where \(k\) is a constant. Given that \(l\) and \(m\) are perpendicular,
  1. find the value of \(k\). [4]
Edexcel C1 Q7
8 marks Moderate -0.3
Given that $$\text{f}'(x) = 5 + \frac{4}{x^2}, \quad x \neq 0,$$
  1. find an expression for \(\text{f}(x)\). [3]
Given also that $$\text{f}(2) = 2\text{f}(1),$$
  1. find \(\text{f}(4)\). [5]
Edexcel C1 Q8
10 marks Moderate -0.8
\(\text{f}(x) = x^3 - 6x^2 + 5x + 12\).
  1. Show that $$(x + 1)(x - 3)(x - 4) \equiv x^3 - 6x^2 + 5x + 12.$$ [3]
  2. Sketch the curve \(y = \text{f}(x)\), showing the coordinates of any points of intersection with the coordinate axes. [3]
  3. Showing the coordinates of any points of intersection with the coordinate axes, sketch on separate diagrams the curves
    1. \(y = \text{f}(x + 3)\),
    2. \(y = \text{f}(-x)\). [4]
Edexcel C1 Q9
11 marks Moderate -0.3
The first two terms of an arithmetic series are \((t - 1)\) and \((t^2 - 5)\) respectively, where \(t\) is a positive constant.
  1. Find and simplify expressions in terms of \(t\) for
    1. the common difference of the series,
    2. the third term of the series. [4]
Given also that the third term of the series is 19,
  1. find the value of \(t\), [2]
  2. show that the 10th term of the series is 75, [3]
  3. find the sum of the first 40 terms of the series. [2]
Edexcel C1 Q10
11 marks Standard +0.3
\includegraphics{figure_1} Figure 1 shows the curve with equation \(y = 2 + 3x - x^2\) and the straight lines \(l\) and \(m\). The line \(l\) is the tangent to the curve at the point \(A\) where the curve crosses the \(y\)-axis.
  1. Find an equation for \(l\). [5]
The line \(m\) is the normal to the curve at the point \(B\). Given that \(l\) and \(m\) are parallel,
  1. find the coordinates of \(B\). [6]